Trunked systems work like this:
You have the system itself. Inside the system you have frequencies that the system is allowed to use; it could be 5 frequencies, 7, 10, 15, even 20 depending on the capacity as well as the needs of the system when it's designed, but future expansion is always a possibility.
One, two, or three of those frequencies (again, depending on the size and capacity) are assigned as
control channels - you need to understand the fundamental difference here between frequency and channel. Frequency would mean the actual radio frequency being put to use for that purpose;
channel would mean the assigned purpose.
To break that concept down, the FCC will license you 10 frequencies, but they could care less what you use the first frequency for, or the second, or the third basically. You come in and say "Ok, let's use this frequency as
channel 1, this as
channel 2, etc. See the difference there? I hope so...
Ok, a
control channel in a trunked system is specifically assigned to do one thing: broadcast the control channel data from the radio system itself to all the radios that are "listening" and part of the system. An analogy would be this:
The human Dispatcher in a system is in charge of assigning jobs, tasks, priorities, needs, etc. That makes sense, right? The Dispatcher calls out and says "Unit XX, go do this" or "Unit YY, switch to channel 4 for further information" etc.
The control channel does the same thing, but instead of telling the actual people on the radio system what to do, what channel to be on, or defining which radio they're assigned,
it's sending those instructions directly to the radios themselves. It's an electronic Dispatcher, somewhat, and the "units" are each and every single radio that's part of that trunked system.
Each and every radio in that system technically has two tuners in it: one is always listening to the control channel
frequency - the one assigned for control channel broadcast purposes (I mentioned the 1, 2, 3, or even more that can be used in systems but typically only 1 control channel is broadcasting at any given time). The other tuner/transceiver is used for the actual voice traffic when the radio owner presses transmit to talk to someone on the system, or when they're listening to activity from Dispatch (the human Dispatcher) or other units in the field, etc.
Ok, because of how a trunked system works, it allows for a great number of actual radio communications to happen at any given time. In the old days, you'd have a system with 3, maybe 4 frequencies in a small town/community. The police might use one of those, the fire dept might use another, local government a third, and the fourth could be used for emergencies. Now consider that in such a situation, only 1 radio communication would happen on each frequency at any given time. In a high stress situation, imagine that if the police frequency was busy with some information traffic (someone running a license plate and needing to transmit all the VIN letters one at a time) and in the middle of that another officer gets in an accident or, heaven forbid, gets shot or something worse.
That officer can't transmit because the frequency is in use, right? Right, it's a bad way of doing things. Then someone came up with the idea of trunked communications. That basically works by having a set of frequencies as I explained above (5, 7, 10, 15, 20 or more) and the radios are designed to "hop" frequencies as needed - they don't remain on a static frequency. In some respects, a lot of trunked radio system technology is borrowed from cellular technology, but proximity to cell towers and signal strength (which is how cell phones "hop" cell sites) don't relate here; trunked systems "hop" frequencies because the control channel tells them to, and which frequency to hop to.
On top of all of this, the additional benefit is that each radio can have a unique digital ID, commonly called an RID (radio ID, go figure). Because of this, you can group radio IDs together into <drumroll please>
talkgroups and each talkgroup can be assigned an ID also. Those TGIDs or TGs for short (talkgroup IDs or talkgroups) are what you were talking about in the OP (original post) above. The 5 digit decimal codes you posted:
13808
13680
13712
are TGIDs for the trunked system you happen to be monitoring. Unfortunately, you neglected to provide us with any more information so, we can't help you identify the TGIDs because we don't know what system you're monitoring, what location or part of the world you're in, the city, state, etc. That info can lead to finding out what those TGIDs are actually assigned for based on the city/state information you can provide and then use to look up the info (probably) in the RadioReference database here at this website/forum.
The beauty of talkgroups is that you can assign a radio to be in that group and then that group communicates with itself: say you wanted a bunch of officers assigned to the southeastern part of the city, you can create a talkgroup for just them and assign it a talkgroup ID of 13808 (I'm just using your first TGID as an example here, bear that in mind) and then label it "Southeast Patrol." Now, when anyone that's in that talkgroup transmits, the only people on the entire trunked radio system that will be able to hear that person talking/transmitting are those with their radios set for the same talkgroup - understand?
When they press the Transmit button, all of this happens in a fraction of a second:
1 - The radio transmits the radio ID and the talkgroup ID to the Dispatch computer
2 - The Dispatch computer checks to make sure the radio is actually part of the system
3 - The Dispatch computer checks for the next open frequency to command all the radios in the same talkgroup to "hop" to so they can monitor what your radio is about to transmit
4 - The Dispatch computer sends out the command (using the control channel) for all radios in the 13808 talkgroup to "hop" to frequency XXX.XXXX and open their squelch so they can listen to the broadcast from your radio
5 - The Dispatch computer sends an OK signal to your radio to begin transmitting its audio signal and then all the others in the talkgroup hear it.
Those 5 basic steps happen every single time someone presses Transmit on a trunked radio system radio. The "OK" signal to transmit is audible on many systems: you can spot it whenever someone keys a mic (presses Transmit) as the "beepbeepbeepbeep" - 4 quick beeps in rapid succession that are usually heard within about 1 second of the person actually pushing the Transmit button. That's their
audible signal from the radio that means "Ok, I just talked with the Dispatch computer and all the other units are now listening, go ahead and talk." Not all systems use it, of course, but a great many do.
A trunked system allows far more people to use a radio system in a vastly more efficient way. In Las Vegas where I live, there's one system here that I monitor constantly that's primarily run by the county itself (Clark County) and there are over 5000 radios on the system, and over 380 talkgroups. That kind of system simply wouldn't be possible on the old 4 frequency/channel "small town" style hardware anymore.
Now, with the trunked system in place, the police depts here all have their own talkgroups, the fire does, the airport here (one of the busiest in the nation) has theirs, local govt, county govt, community service, the jails, detention center, etc - they all use the same radio hardware, just different talkgroups. This has the added benefit that if something major happens, there's no issue with a bunch of different radio systems that can't communicate with each other. Any given unit can be programmed (if it's not already) to switch talkgroups from one purpose to another in an emergency situation, so the cost savings is enormous too.
I've rambled on long enough... if you provide us your city/state, we can probably find out what those talkgroups actually are.
Good luck...